Can I make QuickTime movies play automatically when someone opens the iWeb page they're on?

Find your movie's files under Movie if you didn't rename them in iWeb.

Surprisingly, no - at least not a push-button way. If you're willing to dig into some code, however, you can force iWeb movies to automatically play when the page loads. Roll up your sleeves and launch a text editor - if you use TextEdit (/Applications), launch the app first, select TextEdit > Preferences, and click the Open & Save tab. Put a checkmark in the box labeled Ignore Rich Text Commands In HTML Files. Close the preferences dialog and open your iWeb site folder, either on your iDisk or in the Finder, depending on where you publish your site. For each movie page, iWeb creates a folder called Movie_files, inside of which you'll find a file called Movie.js (if you changed the default page title, use it here in place of Movie). Open the file in your text editor, press Command-F (or Edit > Find > Find), and type autoplay into the search box. When you find it, change the associated value from the default False to True. iWeb uses two types of encoding, so find autoplay again and change the value to True. Note that you'll have to repeat this process every time you publish the site and overwrite your changes, so it'd be worth your while to use TextWrangler (free, www.barebones.com), which has a simple Find & Replace feature you can use to change every instance of Autoplay=false in your iWeb folder.